Flory-Orwoll theory

While the Flory-Orwoll theory for the equation of state of bulk polymers can be employed, a simpler free-volume equation of state is often used in practice. The details of this theory and its application to the description of the viscosity of low-molecular-weight polymer liquids is presented... 

It is not surprising that attempts have been made to derive equations of state along purely theoretical lines. This was done by Flory, Orwoll and Vrij (1964) using a lattice model, Simha and Somcynsky (1969) (hole model) and Sanchez and Lacombe (1976) (Ising fluid lattice model). These theories have a statistical-mechanical nature they all express the state parameters in a reduced dimensionless form. The reducing parameters contain the molecular characteristics of the system, but these have to be partly adapted in order to be in agreement with the experimental data. The final equations of state are accurate, but their usefulness is limited because of their mathematical complexity. 

The cell theory of Prigogine has been applied by Clark and Schmidt and by Hicks and Young to benzene + polyphenyl systems and n-alkane mixtures respectively. The Flory, Orwoll, and Vrij theory has also been applied by Hicks and Young to n-alkane mixtures. 

The first successful theoretical approach of an equation of state model for polymer solutions was the Prigogine-Flory-Patterson theory. It became popular in the version by Flory, Orwoll and Vrij and is a van-der-Waals-like theory based on the corresponding-states principle. Details of its derivation can be found in numerous papers and books and need not be repeated here. The equation of state is usually expressed in reduced form and reads ... 

On the other hand, Sauer and Dee (1994) have demonstrated that, by refining the equation of state used in the gradient theory, by using better experimental data and a different equation of state model, the Flory, Orwoll and Vrij model (the FOV model) (Flory et al. 1964), excellent agreement, at the level of better than 1%, between theory and experiment is obtained. The square gradient coefficient still has to be adjusted somewhat from the mean-field value, but it is still treated as entirely enthalpic in origin, with no temperature dependence. 

Redlich-Kwong equation of state and Soave modification Peng-Robinson equation of state Tait equation for polymer liquids Flory, Orwoll, and Vrij models Prigogine square-well cell model Sanchez-Lacombe lattice fluid theory... 

Nine different equations-of-state, EOS theories are described including Flory Orwoll Vrij (FOV) Prigogine Square Well cell model, and the Sanchez Lacombe free volume theory. When the mathematical complexity of the EOS theories increases it is prudent to watch for spurious results such as negative pressure and negative volume expansivity. Although mathematically correct these have little physical meaning in polymer science. The large molecule effects are explicitly accounted for by the lattice fluid EOS theories. The current textbooks on thermodynamics discuss... 

The first equation-of-state theory developed for polymers was due to Flory, Orwoll and Vrij (1964) and Eichinger and Flory (1968), the so-called FOVE model. Each of the components is characterized by p, V and T obtained from data for the pure components. Two interaction terms, denoted Xj2 and Qi2, associated with the enthalpy and entropy of the mixture, are introduced. The equation of state is ... 

Jo WH, Lee HS, Lee SC (1998) Temperature and molecular weight dependence of inter facial tension between immiscible polymer pairs by the square gradient theory combined with the Flory Orwoll Vrij equation of state theory. J Polym Sci B Polym Phys 36 2683 2689... 

Experimental studies of concentrated polymer soluhons reveal that most binary liquid mixtures display a lower crihcal soluhon temperature. A theory including equahon of state contribuhons was developed by Orwoll and Flory. i This theory is presented and discussed in Sechon 7.5... 

There are several criteria for determining the miscibility in polymer blends. The thermodynamic criteria date back to the seminal studies of Flory (1941, 1942) and Huggins (1941, 1942) in the 1940s. Since then, other thermodynamic theories have been developed (Flory 1965 Flory et al. 1968 Orwoll and Flory 1967 Sanchez and Lacombe 1978) for investigating the phase behavior of polymer blends. As the discussion of thermodydnamic criteria for miscibility in polymer pairs is beyond the scope of this chapter, here we illustrate briefly different phase behaviors of polymer blends in general terms, using examples that will facilitate our presentation in the rest of this chapter. 

Flory PJ, Orwoll RA, Vrij A (1964) Statistical thermodynamics of chain molecule liquids. I. An equation of state for normal paraffin hydrocarbons. J Am Chem Soc 86 3507 3514 Nose T (1976) Theory of liquid liquid interface of polymer systems. Polym J 8 96 113 de Gennes P G (1977) Qualitative features of polymer demixtion. J Phys Lett 38 L441 L443 Ouhadi T, Fayt R, Jerome R, Teyssie Ph (1986) Molecular design of multicomponent polymer systems. 9. Emulsifying effect of poly(alpha methylstyrene b methlyl methacry late) in poly(vinylidene fluoride)/poly(alpha methylstyrene) blends. Polym Commun 27 212 215... 

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